Interpretation methods for NMR diffusion-T2 maps

ABSTRACT

A method is disclosed for interpretation of multi-dimensional nuclear magnetic resonance data taken on a sample of an earth formation. Specifically, a set of NMR data is acquired for a fluid sample located either in a borehole or in a laboratory environment. From the set of NMR data, a multi-dimensional distribution is calculated using a mathematical inversion that is independent of prior knowledge of fluid sample properties. The multi-dimensional distribution is graphically displayed on a multi-dimensional map. Each fluid instance or artifact visible on the graph is identified as representing a probable existence of a detected fluid. One or more quantitative formation evaluation answers for one or more fluid instances is computed based on the multi-dimensional distribution associated with the respective fluid instance.

CROSS-REFERENCE TO RELATED APPLICATIONS

This invention claims priority pursuant to 35 U.S.C. § 119 of U.S.Provisional Patent Application Ser. No. 60/450,412, filed on Feb. 27,2003. This Provisional Application is hereby incorporated by referencein its entirety.

BACKGROUND OF INVENTION

Both water and hydrocarbons in earth formations produce detectable NMRsignals. It is desirable that the signals from water and hydrocarbons beseparable so that hydrocarbon-bearing zones may be identified. However,it is not always easy to distinguish which signals are from water andwhich are from hydrocarbons. Various methods have been proposed toseparately identify water and hydrocarbon signals.

The differential spectrum (DSM) and shifted spectrum (SSM) methodsproposed by Akkurt et. al. in “NMR Logging of Natural Gas Reservoirs”Paper N. Transactions of the Society of Professional Well Log Analysts(SPWLA) Annual Logging Symposium, 1995, compare T₂ distributions derivedfrom two Carr-Purcell-Meiboom-Gill (CPMG) measurements performed withdifferent polarization times (DSM) or echo-spacings (SSM). Amodification to these methods, known as time domain analysis (TDA), waslater introduced by Prammer et al. in “Lithology-Independent GasDetection by Gradient-NMR Logging,” SPE paper 30562, 1995. In TDA,“difference” data are computed directly in the time domain bysubtracting one set of the measured amplitudes from the other. Thedifference dataset is then assumed to contain only light oil and/or gas.In TDA, relative contributions from light oil or gas are derived byperforming a linear least squares analysis of the difference data usingassumed NMR responses for these fluids. Both DSM and TDA assume that thewater signal has substantially shorter T₁ relaxation times than those ofthe hydrocarbons. This assumption is not always valid, however. Mostnotably, this assumption fails in formations where there are large poresor where the hydrocarbon is of intermediate or high viscosity. The SSMmethod and its successor, the enhanced diffusion method (EDM) proposedby Akkurt et. al. in “Enhanced Diffusion: Expanding the Range of NMRDirect Hydrocarbon Typing Applications”, Paper GG. Transactions of theSociety of Professional Well Log Analysts (SPWLA) Annual LoggingSymposium, 1998, separate gas, oil and water contributions based onchanges in the T₂ distributions that result from changes in the echospacing of CPMG measurements. The methods are applicable in a limitedrange of circumstances and the accuracy of the result is significantlycompromised by incomplete separation of water and hydrocarbon signals inthe T₂ domain. Moreover, these methods are designed to function withCPMG sequences. However, with the diffusion-based methods, CPMG pulsesequences provide poor signal to noise ratios due to the reduced numberof echoes that can be measured. A strategy for combining and selectingthese different NMR methods has been described recently by Coates et al.in U.S. Pat. No. 6,366,087 B1.

The diffusion-editing (DE) pulse sequence by Hürlimann et al. provides adifferent approach. See M. D. Hürlimann et al., “Diffusion-Editing: NewNMR Measurement of Saturation and Pore Geometry,” paper presented at the2002 Annual Meeting of the Society of Professional Well Log Analysts,Osio, Japan, June 2-5; see also, U.S. Pat. No. 6,570,382, filed on Nov.28, 2000, by Hürlimann. This patent is assigned to the same assignee asthe present invention and is hereby incorporated by reference.

DE pulse sequences are similar to the CPMG sequences except that theinitial two echoes are acquired with longer echo spacings and the thirdand subsequent echoes are acquired with shorter echo spacings. In DEpulse sequences, diffusion information is encoded during the acquisitionof the first two echoes, whereas the third and subsequent echoes providebulk and surface relaxation time information with relatively littleattenuation of the signal by diffusion. Using a conventional CPMGsequence to encode the diffusion information requires a long inter-echospacing, which results in poor bulk and surface relaxation timeinformation because diffusion decay attenuates the signal afterrelatively few echoes. Consequently, a suite of data acquired with DEsequences provides better diffusion information and signal-to-noiseratio in the spin-echo data, as compared to an analogous suite acquiredwith CPMG sequences. Therefore, DE sequences can provide more accurateand robust computations of brine and oil T₂ distributions than CPMGsequences.

In addition to DE sequences, specialized interpretation methods havebeen developed for NMR data in order to further enhance hydrocarbondetection. These methods typically apply forward modeling to suites ofNMR data acquired with different parameters. The suite of NMR data aretypically acquired with different echo spacings (TE) or polarizationtimes (WT), and sometimes acquired with different magnetic fieldgradients (G). DE sequences are one example of such data acquisition.Two exemplary methods include: the MACNMR proposed by Slijkerman et al.,SPE paper 56768, “Processing of Multi-Acquisition NMR Data”, 1999, andthe Magnetic Resonance Fluid characterization (MRF) method disclosed inU.S. Pat. No. 6,229,308 B1 issued to Freedman and assigned to theassignee of the present invention (“the Freedman patent”). The Freedmanpatent is hereby incorporated by reference.

The MRF method is capable of obtaining separate oil and water T₂distributions. This method uses a Constituent Viscosity Model (CVM),which relates relaxation time and diffusion rates to constituentviscosities whose geometric mean is identical to the macroscopic fluidviscosity. With the MRF method, estimates for water and hydrocarbonvolumes are obtained by applying a forward model to simulate the NMRresponses to a suite of NMR measurements acquired with differentparameters. Specifically, The MRF technique is based on establishedphysical laws which are calibrated empirically to account for thedownhole fluid NMR responses. By using realistic fluid models, MRF aimsto minimize the number of adjustable parameters to be compatible withthe information content of typical NMR log data. Since the modelparameters are by design related to the individual fluid volumes andproperties, determination of the parameter values (i.e. data-fitting)leads directly to estimates for petrophysical quantities of interest.

The forward-model approach relies on the validity of the fluid modelsemployed. In “non-ideal” situations where fluid NMR responses deviatefrom the model behavior (oil-wet rocks, restricted diffusion), thesetechniques may lead to erroneous answers. In some circumstances,“non-ideal” responses may be identified by poor fit-quality, in whichcase the fluid models can be adjusted by modifying the appropriate modelparameter. However, it may not be obvious which element of the fluidmodel should be modified and what modification is needed.

Another approach developed by Schlumberger, based on a maximum entropyprinciple (MEP), consists of a general model-independent method toanalyze complex fluids data acquired with NMR logging instruments andpresent the results in a visually attractive and easy-to-understandformat, hereby referred to as Diffusion-Relaxation maps, or D-T2 maps.These maps have been used to understand cases where model-based analysisgives unsatisfactory results because of deviations of NMR propertiesfrom the “ideal” behavior assumed in the models. These situations canarise due to anomalous fluid/rock interactions such as restricteddiffusion, mixed-wettability and internal gradients. Deviations from thedefault properties have also been observed for certain crude oils,leading to inaccurate predictions in the model analysis. Through the useof D-T2 maps, the MEP approach provides a simple graphicalrepresentation of the data that can be used to identify fluid responsesin all environments. Diffusion-Relaxation maps are further described incommonly assigned U.S. Pat. Nos. 6,570,382 and 6,462,542.

While these prior art methods are useful in predicting the presence ofhydrocarbons in the formations, it is desirable to have simpler methodsthat can predict the presence of hydrocarbons in the formations from NMRdata and are generally applicable to NMR data acquired with differentpulse sequences. Furthermore, while two and three dimensionalvisualization has been developed to obtain primarily qualitativeinformation, it is desirable to have quantitative interpretationtechniques that can provide accurate fluid-characterization results.

SUMMARY OF INVENTION

According to one aspect of the disclosed subject matter a method isdescribed for interpretation of multi-dimensional nuclear magneticresonance data taken on a sample of an earth formation. Specifically, aset of NMR data is acquired for a fluid sample located either in aborehole or in a laboratory environment. From the set of NMR data, amulti-dimensional distribution is calculated using a mathematicalinversion that is independent of prior knowledge of fluid sampleproperties. The multi-dimensional distribution is graphically displayedon a multi-dimensional map. Each fluid instance or artifact visible onthe graph is identified as representing a probable existence of adetected fluid. One or more quantitative formation evaluation answersfor one or more fluid instances are computed based on themulti-dimensional distribution associated with the respective fluidinstance.

According to another aspect, quantitative formation evaluation answersare determined from the multi-dimensional distribution of NMR data byinitially determining a set of model parameters which represent aspectsof the multi-dimensional distribution. A model dependent inversion isthen applied to compute the fluid properties.

According to another aspect, quantitative formation evaluation answersare determined from the multi-dimensional distribution of NMR datathrough a point-and-click approach. One or more fluid artifacts areselected from a multi-dimensional map of the NMR data using a computermouse or an automatic edge selection application. The amplitude isintegrated over the selected region to determine properties of the fluidassociated with the selected region.

According to another aspect, quantitative formation evaluation answersare determined from the multi-dimensional distribution of NMR data bydetermining a mean diffusion value across a region of a diffusion-T2relaxation distribution. The mean diffusion is used to determineproperties of the fluid associated with the selected region.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a diagram of an exemplary downhole nuclear magnetic resonancedata acquisition system.

FIG. 2 is a more detailed diagram of the system of FIG. 1.

FIG. 3 is a multi-dimensional map or graph for displaying NMR data.

FIG. 4 is a NMR data map showing non-ideal effects on the NMR data.

FIG. 5 is another NMR data map showing non-ideal effects on the NMRdata.

FIG. 6 is another NMR data map showing non-ideal effects on the NMRdata.

FIG. 7 is another NMR data map showing non-ideal effects on the NMRdata.

FIG. 8 is two dimensional graph according to a prior art inversionmethod.

FIG. 9 is a NMR data map set showing correction of non-ideal effectsaccording to one aspect of the disclosed subject matter.

FIG. 10 illustrate a correction of a prior art inversion methodaccording to the NMR data map set of FIG. 9.

FIG. 11 is two dimensional graph according to a prior art inversionmethod.

FIG. 12 is a NMR data map set showing correction of non-ideal effectsaccording to one aspect of the disclosed subject matter.

FIG. 13 illustrate a correction of a prior art inversion methodaccording to the NMR data map set of FIG. 12.

FIG. 14 is a set of NMR maps and graphs according to one formationevaluation method of the disclosed subject matter.

FIG. 15 is a flow diagram of the method illustrated in FIG. 14.

FIG. 16 is a multi-dimensional map or graph of another formationevaluation method of the disclosed subject matter

FIG. 17 is a set of NMR maps and graphs according to the methodillustrated in FIG. 16.

FIG. 18 is a flow diagram of the method illustrated in FIGS. 16 and 17.

FIG. 19 is another set of NMR maps and graphs of a formation evaluationmethod of the disclosed subject matter.

FIG. 20 is a set of corrected NMR graphs according to the methodillustrated in FIG. 19.

FIG. 21 is a screen shot illustrating exemplary formation evaluationanswers provided by the disclosed subject matter.

DETAILED DESCRIPTION

The disclosed subject matter describes quantitative methods to interprettwo-dimensional nuclear magnetic resonance (NMR) maps derived fromcommon NMR formation evaluation measurements. Although other values maybe used, a preferred embodiment is primarily discussed herein based ondiffusion vs. T₂ (D-T2) maps. According to the present invention, D-T2maps can be used to help in the selection of parameters for applicationto existing model-based inversion codes. Further, complete petrophysicalanswers (porosity, permeability, fluids volumes, saturations, oilviscosity etc.) can be derived directly from the D-T2 maps. To takeadvantage of the visual appeal of the maps, the proposed methods areinteractive and, according to an embodiment, consist of sequentialpoint-and-click procedures.

Acquisition of NMR measurements according to embodiments of theinvention may be accomplished with various methods of NMR measurementsknown in the art. For example, the measurements may be performed in alaboratory using a sample removed from an earth formation.Alternatively, the NMR measurements may be performed in a loggingoperation using a wireline tool, a logging-while-drilling ormeasurement-while-drilling tool, or a formation tester. FIG. 1illustrates a schematic of an NMR logging system. In FIG. 1, a NMRlogging tool 30 for investigating earth formations 31 traversed by aborehole 32 is shown. The NMR logging device 30 is suspended in theborehole 32 on an armored cable 33, the length of which substantiallydetermines the relative axial depth of the device 30. The cable lengthis controlled by suitable means at the surface such as a drum and winchmechanism 8. Surface equipment 7 can be of conventional type and caninclude a processor subsystem which communicates with downhole equipmentincluding NMR logging device 30.

The NMR logging device 30 can be any suitable nuclear magnetic resonancelogging device; it may be one for use in wireline logging applicationsas shown in FIG. 3, or one that can be used in logging-while-drilling(LWD) or measurement-while-drilling (MWD) applications. In addition, theNMR logging device 30 may be part of any formation tester known in theart, such as that sold under the trade name of MDT™ by SchlumbergerTechnology Corporation (Houston, Tex.). The NMR logging device 30typically includes a means for producing a static magnetic field in theformations, and a radio frequency (RF) antenna means for producingpulses of magnetic field in the formations and for receiving the spinechoes from the formations. The means for producing a static magneticfield may comprise a permanent magnet or magnet array, and the RFantenna means for producing pulses of magnetic field and receiving spinechoes from the formations may comprise one or more RF antennas.

FIG. 2 illustrates a schematic of some of the components of one type ofNMR logging device 30. FIG. 4 shows a first centralized magnet or magnetarray 36 and an RF antenna 37, which may be a suitably oriented coil orcoils. FIG. 2 also illustrates a general representation ofclosely-spaced cylindrical thin shells, 38-1, 38-2 . . . 38-N, that canbe frequency selected in a multi-frequency logging operation. One suchdevice is disclosed in U.S. Pat. No. 4,710,713. In FIG. 2, anothermagnet or magnet array 39 is shown. Magnet array 39 may be used topre-polarize the earth formation ahead of the investigation region asthe logging device 30 is raised in the borehole in the direction ofarrow Z. Examples of such devices are disclosed in U.S. Pat. Nos.5,055,788 and 3,597,681.

Turning now to FIG. 3, shown is an exemplary D-T2 map with NMR spin echodata presented as amplitudes versus diffusion (D) and relaxation (T2).The map shown in the left panel is a three-axis perspective view. Theright panel provides a more practical representation of D-T2 map as atwo-axis map. However, it should be noted that the disclosed methods maybe applied a dataset having any number of dimensions, 2-D, 3-D, 4-D,etc. Furthermore, it should be noted that although D-T2 maps arediscussed herein for exemplary purposes, the disclosed methods can beequally as effective in obtaining quantitative formation evaluationanswers based on many other combinations of NMR data properties (D, T1,T2, T1/T2, etc.).

In the context of the two-axis D-T2 map, the diffusion amplitude isrepresented according to a color-coding scheme. The differences ofdiffusion properties among gas, water and various viscosity oils arecaptured by the D-T2 map and shown as separate and distinct peaks.Specifically, the color grouping at A, also herein referred to as anartifact or a fluid instance, represents the probable detection of afirst fluid. Similarly, the lighter color groupings or fluid instancesat B, C and D also represent the probable detection of three additionalfluids. The theoretical responses of water, oil, and gas are overlaid onthe maps to help the interpretation. Thus, for grouping or instance A,it is likely that the fluid is gas because its peak lies near thetheoretical gas diffusion value. For groupings B and C, it is likely thefluids are varying viscosities or phases of oil, lying along thetheoretical oil diffusion line. Finally, it is likely that grouping orinstance D is water subject to restricted diffusion (discussed below).

According to one embodiment, the cross-plot of FIG. 3 ismodel-independent. This means that no predetermined diffusion values orlimits are imposed in the calculation to obtain NMR measurements fromthe spin echo data. Although others exist, one example of amodel-independent calculation is the previously mentioned MEP approach.Returning to FIG. 3, in order to assist interpretation of the NMR data,an overlay of theoretical responses of water, oil and gas is helpful.

As mentioned, previous attempts to determine quantitative formationevaluation answers have been based on the model predetermined values ofdiffusion and T2 relaxation parameters of the fluids. In addition, ithas been required to select a fluid model based upon a best guess as towhich fluids will be detected. Needless to say, any inaccuracies in theinitial estimates of the fluid model and the fluids parameters createinaccuracies in the final answers. FIG. 4 graphically illustrates someexceptions to common ideal models: 1) Internal gradient pulls data inthe up-arrow direction (such that water could be mistaken for gas), 2)Restricted diffusion pulls data in the other direction as indicated bythe down arrow (such that water could be mistaken for oil), 3) Mixedwettability pulls the oil data to the left (such that the oilvolume/saturation are computed too low), and 4) high GOR (Gas Oil Ratio)cause oils to shift along the North-East trend (such that oils could bemistaken for water or gas).

For example, FIG. 5 illustrates an effect of internal gradient effect ona NMR fluid response. The internal gradient adds to the tool gradientand hence, diffusion is higher than expected. The sample is a clay-richsandstone in a known water-bearing zone of a well drilled withwater-base mud. As such, the calculated diffusion values appear higherthan the expected result, indicated by the water diffusion line overlay.

Another example is shown in FIG. 6, which illustrates an effect ofrestricted diffusion in a known carbonate dominated formation. The freewater undergoes unrestricted diffusion in large pores and agrees withthe theoretical response. The bound water is trapped in smaller poresand therefore experiences restricted diffusion. The result is one peak,representing the free water, at the expected water diffusion overlay anda second peak, representing the bound water, stretched across a range ofdiffusion values, even crossing into values indicative of hydrocarbonpresence.

Yet another example, shown in FIG. 7, illustrates gas inhigh-permeability sandstone reservoirs in the Middle East. The largepore sizes cause the water to relax close to its bulk value overlappingthe gas signal, and resulting in a smeared peak at a long T2.

According to an embodiment of the present invention, these D-T2 maps aregenerated by model-independent inversion codes such as MEP. These modelindependent inversions do not require a priori input of the fluidsdiffusion or T2 values. According to one embodiment, the modelindependent inversions do not require any a priori knowledge of fluidproperties nor what fluids are present. From these inversions, D-T2 mapsor graphs are generated to display the resultant multi-dimensional NMRdata across two, three or more axes in an easily readable form.

According to one embodiment, the D-T2 maps are used to improve theresults of model-dependent inversion such as the MRF analysis.Specifically, MEP, and other model independent derived D-T2 maps providean unbiased representation of the NMR data. As such, an overlay of thetheoretical responses of the three most encountered fluids, i.e., water,oil, and gas indicates whether the responses need adjustments for use inmodel-based inversion.

For example, the MRF model (for oil, gas and water) states that thewater and gas diffusion constants are independent of T2, and depend ontemperature T and pressure P (for gas):D _(W)(T2)=D _(W)(T)  (1)D _(g)(T2)=D _(g)(T,P)  (2)For oil, the diffusion constant is linearly proportional to T2,D _(O)(T2)=λ×T2  (3)

It follows from Equations (1)-(3) that two horizontal lines (i.e. atconstant D values) representing the theoretical responses of water andgas, and a diagonal line representing the theoretical response of oilcan be overlaid on a D-T2 map. Deviations from the ideal fluid responseswill be evident in the maps as signals located away from the overlaylines. Once known, these deviations are applied to the model-basedinversion. The result from the inversion provides an answer withimproved accuracy based on the observations from the model-independentD-T2 maps.

FIGS. 8-10 illustrate the model-dependent inversion correction in awater based drilling fluid, cesium formate, and FIGS. 11-13 illustratethe correction in a primarily crude oil sample. FIG. 8 shows anexemplary model dependent based analysis, such as the MRF approach, fora cesium formate solution. FIG. 8 shows the model-based analysis havingan oil peak 200 and a water peak 201. The model based analysis using thedefault water diffusion constant indicates mostly oil for cesium formatedrilling fluid. FIG. 9 shows the D-T2 map on the left for the same datahaving the fluid instance or artifact 206 lying along the default oildiffusion line 204. Specifically, the D-T2 map on the left shows thatthe detected Cs formate fluid, the instance 206, has a much lowerdiffusion constant than pure water (the default), indicated byhorizontal line 202. Thus it can be determined that the ideal waterdiffusion 202 is not correct for the Cs formate sample. Thus, in orderto compute correct fluid saturations the effective “water” (Cs formateto be precise) diffusion constant must be reduced to 40% of its defaultvalue, represented by horizontal line 208. This corrected diffusionvalue is then programmed into the model based inversion. FIG. 10 showsthe reprocessed MRF results obtained using a water diffusion constantreduced to 40% of its original value. The MRF results now correctlyindicate predominantly water, shown at peak 210, having a very low oilsignal, shown at peak 212. As such, the associated formation evaluationdeterminations such as water volume and saturation can be moreaccurately computed.

FIG. 11 shows a model dependent based analysis of a known crude oilsample. The results indicate the presence of oil, shown by peak 220, butalso incorrectly indicates significant water saturation, indicated bypeak 221. FIG. 12 shows the D-T2 map for the same data. On the left, theD-T2 map is shown with the default fluid overlay lines, the waterdiffusion represented by horizontal line 222 and the oil diffusionrepresented by line 224. The signal or instance 226 appears above theoil D-T2 correlation line 224 indicating that this oil has an unusuallyhigh diffusion to T2 ratio. Thus, it can be determined that the existingoil D-T2 line 224 is incorrect and requires adjustment. The same map isplotted on the right with a new oil D-T2 correlation line 228 thatbisects the main signal peak. The MRF analysis is then run using anincreased λ value (see Eq (3)). The results of the reprocessed data areshown in FIG. 13. As expected, the MRF analysis now correctly predictspredominantly oil at peak 232, while indicating a very low waterpresence at curve 230.

In addition to assisting model-dependent interpretation techniques asshown above, complete quantitative petrophysical answers can be deriveddirectly from the two-dimensional maps. Specifically, according to oneapplication of the invention, quantitative measurements of porosity,permeability, fluid volumes, saturations, oil viscosity and otherquantities can be derived from D-T2 maps. Compared to prior methods,additional interpretation is needed to derive more than previouslyutilized qualitative information. According to the disclosed subjectmatter, two approaches, a point-and-click approach and a diffusion logmean approach, are used to obtain quantitative answers.

According to one embodiment, a visual point-and-click approach isprovided which allows a user to interact with a D-T2 map by focusing inon particular artifacts graphically shown on a map. The signalamplitude, A, from a suite of NMR pulse sequences can be expressed as$\begin{matrix}{{A\left( {{WT},{TE},t} \right)} = {{\sum\limits_{i}{\sum\limits_{j}{\sum\limits_{k}{{f\left( {i,j,k} \right)}{H\left( {{WT},{TE},{t;i},j,k} \right)}}}}} + {\delta\left( {{WT},{TE},t} \right)}}} & (4)\end{matrix}$where WT, TE, t are the wait time, echo spacing and time of the NMRpulse sequences, (i, j k) are the indices of the T2, D and T1/T2distributions, f(i,j,k) is the amplitude of the three-dimensionalcomponent in the T2, D, T1/T2 space, H(WT, TE, t, i, j, k) is the kernelof that component, and δ is a noise term.

From the above equation (4), it can be seen that the D-T2 map is arepresentation of the signal amplitudes integrated across the kdimension (T1/T2) of the MEP inversion result. Therefore, in thefavorable case where the fluids distributions in the D-T2 space are wellseparated as seen in FIG. 14, their respective volumes can be directlyobtained by integrating the amplitudes in the D and T2 windows definedby each type of fluid. The respective saturations can then be derived bydividing the respective fluid volumes with the total fluid volume. Theindividual volumes must be corrected for hydrogen index, according toknown methods, to give correct answers.

FIG. 14 illustrates an example according to one embodiment of thepoint-n-click approach having four fluids artifacts, 240, 242, 244 and246, that are well separated in D-T2 space (top left pane). Note thatthe four fluids are not resolved in either T2 space (bottom left pane)or D space (top right pane). Specifically, the T2 and D space graphsindicate three instead of four fluids having separable properties. Inthe bottom left T2 graph, peak 248 corresponds to artifact 246 and peak250 corresponds to artifact or fluid instance 244. However, peak 252cannot resolve artifacts 240 and 242. In the top right diffusiondistribution, peak 254 corresponds to artifact 240 and peak 256corresponds to fluid instance 242. However, peak 258 cannot resolveartifacts 244 and 246.

According to prior methods, quantitative fluid answers could be obtainedusing T2 graphs. However, as shown, in some cases T2 maps cannot fullyresolve multiple fluids having different diffusion properties. Knownprior methods have gone a step further to use the D-T2 map to evaluatethe accuracy (qualitatively) of the answers derived from the T2 graphs.According to an embodiment of the present invention, a visualpoint-n-click method uses the D-T2 map to determine quantitatively therespective volumes of each of the four fluids by integrating the signalamplitudes along T2 and D dimensions in the windows defined by therectangles 260, 262, 264 and 266. Note that the use of other shapes todelineate the map region of interest, such as polygons or circles, maybe employed in a similar manner. In this way, the disclosed methodsadvance the state of the art in part by resolving multiple fluids havingsimilar T2 distributions and determining quantitatively certainformation evaluation answers once the fluid artifacts are separatelyidentified.

According to one application of the point-and-click method, theinterpreter can easily select the integration region of the D-T2 mapusing, for example, the computer mouse or a digitized pen. Selection ofa region may also be performed automatically by a software algorithm,for example, based on a predetermined amplitude threshold. Note alsothat the interpretation of the fluid type is guided by overlaying thetheoretical responses of gas, oil and water in the D-T2 map as seen inthe top left pane. This step also may be performed automatically by asoftware application, for example, based on a proximity of a point ofmaximum amplitude to the theoretical gas, oil and water responses.

Turning to FIG. 15, illustrated is a flow diagram of the point-n-clickapproach. Beginning at step 500, the point-and-click routine begins witha D-T2 map. As mentioned, this D-T2 map is preferably generated using amodel-independent inversion approach. Continuing at step 502, the useris asked to enter the type of fluid model to be used in the calculation.Typically, this will be done by inspection of the map. First, the userdecides on the number of fluids. For example, if two amplitude clusters(bright spots) are present, then a two-fluid approach is chosen. Second,each fluid type is interpreted with the help of the overlay oftheoretical responses of water, oil and gas. At step 504, the userselects the fluid region using a computer mouse. According to oneembodiment, a box is displayed and manipulated to encompasssubstantially all the artifact on the D-T2 map. According to aembodiment, the final unselected region having a positive non-zeroamplitude is accumulated and displayed to provide an indication to theuser as to whether any substantial portions had been missed. Accordingto another embodiment, a computer or software application selects anextent at least partially surrounding of each fluid instance based on athreshold amplitude.

Once the artifact has been selected, the fluid volume and saturation iscalculated at step 506 by integrating over the selected region of theD-T2 map. Since the integration over the total map area gives totalporosity, individual fluid saturations can be computed by dividing thefluid volumes with total porosity. It is appropriate to reiterate herethat although the disclosed point-and-click method is discussed forexemplary purposes in the context of D-T2 maps, nearly anymulti-dimensional map can be employed to determine a quantity ofinterest. Continuing at step 510, once fluid volume and saturationquantities, or other base values, have been determined, auxiliarycomputations at 510 can be requested by the user or automatically by thealgorithm. For example, at step 512, viscosity can be determined bycomputing the mean T2 in the oil window, and using published oilviscosity-relaxation charts to estimate viscosity. Another example is touse the map-derived bound fluid volume to compute Timur-Coatespermeability according to the equation k_Timur=a * phit ˆb *((phit−bfv)/bfv) ˆc, where a, b, c are constants, phit is totalporosity, and bfv is the bound fluid volume.

A second approach to directly determine quantitative results from D-T2maps involves a determination of log-mean diffusion (D_(LM)). Instandard MRF analysis, the raw data is fit directly using theconstraints of Eqs. 1, 2 and 3. Similar constraints are imposed forother prior art model dependent inversions. An alternative approach, asdisclosed herein is to use the maps themselves as input to derive thesolution which MRF attempts. Since the information contained in the mapsis essentially identical to that of the original data, the two methodsof solution should be comparable. In practice, however, the data isoften lacking in diffusion information and therefore, the differentfluids D-T2 amplitudes are spread over large areas of the map(resolution). This is in contrast to the ideal situation for applicationof the point-and-click method where each fluid artifact is substantiallyseparated from other fluid instances. The problem then consists ofre-assigning the amplitude spread in the diffusion axis to the differentformation fluids. According to this second approach, an approximate wayto do this is to use the geometric mean diffusion rate for each T2 ,notated D_(LM)(T2), computed from the maps, and redistribute theamplitude at this T2 according to the chosen fluid model. For example,for a model consisting of water and oil it is convenient to define anapparent water saturation at each T2 value, SXO(T2),D _(LM)(T2)=D _(W)(T2)^(SX0(T2)) D _(O)(T2)^(1-SX0(T2))  (5)$\begin{matrix}{{{SX}\quad 0\left( {T\quad 2} \right)} = \frac{\ln\quad\left( {{D_{LM}\left( {T\quad 2} \right)}/{D_{O}\left( {T\quad 2} \right)}} \right)}{\ln\left( {{D_{W}\left( {T\quad 2} \right)}/{D_{O}\left( {T\quad 2} \right)}} \right)}} & (6)\end{matrix}$Separate water and oil T2 distributions, F_(H20), and F_(OIL), can nowbe derived,F _(H2O)(T2_(i))=SX0(T2)×F(T2_(i))  (7)F _(OIL)(T2_(i))=(1−SX0(T2_(i)))×F(T2_(i))  (8) $\begin{matrix}{{F\left( {T\quad 2_{i}} \right)} = {\sum\limits_{j}{\sum\limits_{k}{F\left( {{T\quad 2_{i}},D_{j},{T\quad{1_{k}/T}\quad 2_{k}}} \right)}}}} & (9)\end{matrix}$

The D_(LM) approach is most effective when the fluid model has only 2components. In such a case, a best guess of the fluid model is providedto the software algorithm. In the case of a model involving more than 2components, the extra components are successively eliminated from theD-T2 map. For example, for a water-oil-gas model, the gas component canbe eliminated from the map using the Visual-Point-and-Click approach asdescribed above and the D-T2 map re-normalized for the water-oil model.In practice, because the formation always contains irreducible (bound)water, the final reduced model is either water-oil or water-gas.

FIG. 16 illustrates a graphical representation of an exemplary D_(LM)approach. Here, the D-T2 map shows two different fluid instances. Thefluid instance or artifact 304 is likely oil due to its proximity on thetheoretical oil response overlay 306. According to one embodiment,quantitative evaluation of fluid instance 304 can be determined directlyfrom the D-T2 using the above described point-and-click method. In thiscase, after artifact 304 has been evaluated, it can be deleted and themap renormalized containing only the fluid instance 302. However, sinceartifact 304 is not well separated from artifact 302, the results of thepoint-and-click depend greatly on the delineation process. In anotherembodiment, the D_(LM) approach may include both fluid instances 302 and304. Turning attention to fluid instance 302, the analysis is not asclear. Specifically, the distribution associated with fluid instance 302lies between what one would expect for either water or oil, indicated bythe water overlay 308 and the oil overlay 306. Further, because thefluid type cannot be determined, any integration over the distributionwould not provide accurate formation evaluation answers. A solution,according to one embodiment, is to compute the mean diffusion D_(LM) 312across the distribution 302. Each value of D_(LM) is then used tore-assign the signal amplitude according to the separate fluid diffusionrates as indicated by Eq. 6. The re-assignment is linear in log spaceand based on the proximity with respect to the fluids diffusionsresponses. For example, if log(D_(wat))=a, log(D_(oil))=b, and D_(LM)=c,then the water saturation is S_(W)=(c−b)/(a−b).

FIG. 17 provides another example using the D_(LM) approach derived for aD-T2 map distribution. Here again, the prior art T2 graph cannot resolvethe fluid type of instance 302. Specifically, according to priormethods, the T2 graph at the bottom-left panel shows only the totalcurve 322 (curves 324 and 326 are computed using the methods disclosedherein). Furthermore, the diffusion distribution graph in theupper-right panel similarly cannot resolve more than one fluid type asindicated by diffusion curve 320. According to the disclosed D_(LM)approach, the D_(LM) is multiplied by the overall T2 distribution as perEqs 7 and 8 to yield the water distribution 324 and oil distribution 326seen in the bottom left panel. Integrations of the water and oildistributions then give the water volume (PhiW) and the oil volume(PhiO) seen in the bottom right pane. The oil log mean T2 can also becomputed from the oil distribution (vertical dash line) from which theoil viscosity is estimated (Vis).

FIG. 18 shows a flow chart of an exemplary method employing a D_(LM)determination. Beginning at step 800, a D-T2 map is generated orimported from a model independent inversion process. At step 802, afluid model is selected by the user based in part on a visual inspectionof the D-T2 map or prior knowledge of the sample, or a combination ofboth. The most common fluid models include water-oil or water-gas,although other combinations are equally applicable. Additionally at step802, any fluid artifacts not included in the selected fluid model, butpresent on the D-T2 map, are removed from the distribution. This mayeither be performed manually using a computer mouse, for example, orautomatically by software based on the proximity of an unwanted artifactto the theoretical response of the fluid that is not part of the model.For example, for a selected water-oil model, software can detect that aconcentration of amplitude, indicating the likely presence of a fluid,occurs near the theoretical gas response. An edge-detection routine isexecuted to determine the extent of the artifact, interpreted as a gas,and then delete that region of the map from the total distribution.

Once the unwanted artifacts have been removed, the D-T2 map at step 804is normalized to the selected two-fluid model. At step 806, the log meandiffusion is calculated over the extent of the amplitude concentration.According to one embodiment, the D_(LM) curve is displayed as an overlayon the D-T2 map. From there, and as described above, the fluid volumeand saturation is determined at step 808 using Eq. 6 and 7. Continuingat step 810, the volume and fluid saturation indications are adjusted byfocus windowing to improve the accuracy of the evaluation answers.Specifically, window focusing is performed to impose a saturation value,over a T2 region, in effect overriding the saturation computed by DLM.This is preferred to counteract the unwanted effects of restricteddiffusion, internal gradients etc. mentioned before. Finally, at step812, once fluid volume and saturation quantities, or other base values,have been determined, auxiliary computations at 510 can be requested bythe user or automatically by the algorithm. For example, at step 512,viscosity can be determined by computing the mean T2 of the oildistribution and using published oil viscosity-relaxation charts toestimate viscosity.

It should be noted that the above described exemplary approaches,including the point-and-click method and the D_(LM) method may beemployed on variations of the D-T2 maps. For example, it can be helpfulto define a D-T2 map for a certain T1/T2 ratio. In the context of thepoint-and-click method, the D-T2 inversion results are normallyintegrated over the third dimension which is T1/T2 ratio. However, it isalso possible to decompose the total signal into separate resultscorresponding to each T1/T2 value and benefit from T1 information in thefluid interpretation. Essentially, this means that a D-T2 map isgenerated for each T1/T2 plane.

FIG. 19 provides an example where elimination of one fluid phase isnecessary so that the D_(LM) approach can be applied. The D-T2 map inthe top left panel is derived from the D-T2 map shown in FIG. 14. Thegas peak 240 has been eliminated from the original map of FIG. 14 usingthe visual point-and-click approach and the remaining amplitude issubsequently re-normalized to give the new map shown in FIG. 19.Specifically, the re-normalized map shows artifacts 242′ and 244′, bothbelieved to be oils, and artifact 246′, believed to be water butunclear. Note the absence of the gas diffusion amplitude 254 in the topright pane. Here again, neither diffusion peak 256′ and 258′ fullyresolve any of the artifacts. Specifically, each diffusion peak containsinformation from multiple artifacts, peak 258′ containing informationfrom fluid instances 244′ and 246′, and to a lesser degree, peak 256′containing information from fluid instances 242′ and 246′. Initial fluidvolumes and saturations are displayed in the bottom right pane. However,from the D-T2 map and the T2 graph showing an estimated oil peak 248 aand an estimated water peak 248 b, it is apparent further interpretationis needed to better determine the fluid type associated with artifact246′.

In FIG. 20, the peak appearing at short T2 (˜5 ms), peak 248′ in FIGS.14 and 19 is believed to be water. The breadth of the peak in the D-T2map reflects the uncertainty in the corresponding diffusion rate. Thisis due to lack of information in the original NMR data. With a prioriknowledge we can manually assign this peak as water using the windowfocusing method, resulting in peak 248″. Having done this, the watervolume, oil volume and the T2 log mean of oil have changed compared totheir initial values shown in FIG. 19.

FIG. 21 shows an example of interactive computation of the two oilviscosities that correspond the two bright spots along the oil responseline 247 and 247′ on D-T2 map (FIGS. 14 and 19). Timur-Coatespermeability is also computed interactively for a user-defined T2cutoff.

While the invention has been described with respect to a limited numberof embodiments, those skilled in the art, having the benefit of thisdisclosure, will appreciate that other embodiments can be devised whichdo not depart from the scope of the invention as disclosed herein. Forexample, embodiments of the invention may be practiced with a wirelinetool as well as a LWD or MWD tool. In addition, embodiments of theinvention may be practiced on a fluid sample removed by a formationtester and the NMR measurements are either acquired in the formationtester or in a laboratory. Further, the disclosed methods are notacquisition specific and may be applied to nearly all datasetsregardless of whether a CPMG, diffusion editing or other pulse sequenceis used. Accordingly, the scope of the invention should be limited onlyby the attached claims.

1-8. (canceled)
 9. A method for determining quantitative formationevaluation results from a multi-dimensional representation of nuclearmagnetic resonance data, the method comprising the steps of: Obtaining aset of NMR data for a fluid sample; Computing from the set of NMR data amulti-dimensional distribution using a mathematical inversionindependent of prior knowledge of fluid sample properties; Displayingthe multi-dimensional distribution as an at least two-axis graph;Identifying at least one fluid instance on the graph representing aprobable existence of a detected fluid; and Applying a fluid responsemodel to calculate quantitative formation evaluation values of the fluidsample, the fluid response model being based on the at least one fluidinstance.
 10. The method of claim 9, wherein the mathematical inversionis based on a maximum entropy process.
 11. The method of claim 9,wherein the multi-dimensional distribution is displayed along a fluiddiffusion axis and a T₂ relaxation axis.
 12. The method of claim 11,wherein the graph includes an overlay with ideal diffusion and T₂relaxation values.
 13. The method of claim 11, wherein the identifyingstep further comprises the step of: Determining a diffusion valueassociated with the at least one fluid instance; and Determining a fluidtype associated with the at least one fluid instance.
 14. The method ofclaim 13, wherein the model is in part based on the diffusion value andthe fluid type.
 15. The method of claim 9, further comprising the stepof identifying for additional fluid instances.
 16. The method of claim9, wherein the formation evaluation values are quantitative valuesassociated with the fluid instance of at least one of fluid volume,saturation, viscosity, porosity, and permeability. 17-31. (canceled)